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Math Help - Find the DE that is consistent with this method

  1. #1
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    Find the DE that is consistent with this method

    How do I find a DE that is consistent with:

    u_j^{n+1}=\frac{1}{2}(u_{j+1}^n+u_{j-1}^n)-\frac{1}{2}\frac{\Delta t}{(\Delta x)^3}(u_{j+2}^n-2u_{j-1}^n-u_{j-2}^n)

    Also, when is the scheme stable?
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  2. #2
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    Re: Find the DE that is consistent with this method

    Are you sure about that (\Delta x)^{3} ?
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  3. #3
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    Re: Find the DE that is consistent with this method

    Yes I am :\
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  4. #4
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    Re: Find the DE that is consistent with this method

    Too bad, (\Delta x)^{2} and I could probably offer some help. I'm not familiar with methods involving (\Delta x)^{3}.
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  5. #5
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    Re: Find the DE that is consistent with this method

    can you offer your help for the x^2? And I'll see what I can do to change it for x^3?
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  6. #6
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    Re: Find the DE that is consistent with this method

    It's just textbook stuff. Look at the section on the solutions of parabolic equations.
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